Which one of these cards would be better for playing BF3 multiplayer at 1920x1080 on high or medium settings? I am using an Intel Core i3 2100 (Dual core, 4 threads - Hyperthreading), would either of these cards be bottlenecked by the CPU when playing BF3? I am using a Cooler Master eXtreme Power 500W PSU, I know it's not the greatest and would this PSU run these cards because I am thinking of getting a Corsair Enthusiast 650W Power Supply.
GTX660 is a half tier up from the 7850. It's closer to a 7870. Also Nvidia cards run BF3 just a little better in most cases, so in this case the GTX660 is probably the clear choice. I'd also consider the 7870 if the GTX 660 is in your price bracket.
The CM "Extreme" Power is among their worst. I'm not sure it will safely power either card, at least not for long. If it is good for its label (unlikely, but the 500W Extreme Power "Plus" actually is), it probably has noise and ripple over the ATX specifications (like the aforementioned model) and is very inefficient.